PROJECT SUMMARY: Single particle tracking (SPT) is a powerful class of techniques for understanding biomolecular motion at the subcellular level in the crowded environments of the plasma membrane, cytoplasm, and nucleus. The basic scheme is to acquire image sequences, typically through wide-?eld ?uorescence imaging, produce trajectories from these images, and ?nally to estimate motion parameters from the trajectories through the use of tools such as curve-?tting to the mean-square displacement (MSD) curve. The method has been extremely effective for the study of single particles moving in the plane under a ?xed model. SPT will have a transformative impact once it is capable of studying biological macromolecules moving in three dimensions and undergoing complex modes of motion that switch between different models during a single run as particles undergo, for example, internalization, recycling, and traf?cking between cells. In the 3-D setting, the assumptions that make the standard methods both simple and robust no longer hold and issues such as motion blur, ad hoc choices of ?tting parameters that have a large impact on the accuracy of results, an assumption of stationarity in the data which precludes analysis of mode switching in a single trajectory, separation of the analysis of particle trajectory from motion parameter estimation, and lack of modeling of effects of non-Gaussian noise must be addressed and overcome to make SPT as effective in 3-D as it has been in studying planar motion. The proposed project consists of three speci?c aims. The ?rst is focused on creating techniques for jointly estimating particle trajectory and motion parameters from SPT data sets using a framework that allows for complex motion and observation models, including camera-speci?c descriptions, depth-dependent point spread functions, and dynamics that switch between different models. The resulting method will greatly improve the accuracy and applicability of SPT in the 3-D setting. The second aim targets data acquisition, using a confocal- based tracking scheme inspired by nonlinear, stochastic extremum-seeking control. The confocal modality provides a better SNR, innate 3-D capability and, most signi?cantly, an extremely fast sampling rate to miti- gate effects of motion blur. The proposed method, implementable on standard confocal instruments, is tunable for optimal performance at different experimental settings and complements wide-?eld techniques when high temporal resolution of a single particle is needed. Finally, the third aim seeks to validate the proposed tech- niques in two experimental systems. The ?rst is a simple setting of tracking quantum dots inside hydrogels. These polymer-based systems are extensively used in a number of biomedical applications, including tissue engineering, drug delivery, and immunoisolation. The second setting is that of tracking individual, labeled AMPA receptors in rat hippocampal neurons, providing a biological setting for validation and demonstration.